22 CHAPTER 1 The Real Number System
OBJECTIVES A variableis a symbol, usually a letter such as
x, y,orz, Variables
used to represent any unknown number. An algebraic expressionis a sequence of
numbers, variables, operation symbols, and/or grouping symbols formed accord-
ing to the rules of algebra.
x+5, 2 m- 9, 8 p^2 + 61 p- 22 Algebraic expressions
Variables, Expressions, and Equations
1.3
1 Evaluate algebraic
expressions, given
values for the
variables.
2 Translate word
phrases to algebraic
expressions.
3 Identify solutions of
equations.
4 Identify solutions of
equations from a
set of numbers.
5 Distinguish between
expressionsand
equations.STUDY SKILLS
Study the set of sample math notes given here.
N Include the date and titleof the day’s lecture topic.
N Include definitions,written here in parentheses—don’t
trust your memory.
N Skip lines and write neatlyto make reading easier.
N Emphasize direction words (like simplify) with their
explanations.
N Mark important concepts with stars, underlining, etc.
N Use two columns, which allows an example and its
explanation to be close together.
N Use brackets and arrowsto clearly show steps, related
material, etc.With a partner or in a small group, compare lecture notes.
- What are you doing to show main points in your notes
(such as boxing, using stars, etc.)? - In what ways do you set off explanations from worked
problems and subpoints (such as indenting, using arrows,
circling, etc.)? - What new ideas did you learn by examining your class-
mates’ notes? - What new techniques will you try in your notes?
Taking Lecture Notes
2 mmeans
the product of
2 and m.2 #m, means
the product of 6
and p- 2.6( p-2)OBJECTIVE 1 Evaluate algebraic expressions, given values for the
variables. An algebraic expression has different numerical values for different values
of the variables.
January 2
Exponents
Exponents used to show repeated multiplication.ReadSimplifying an expression with exponents
actually do the repeated multiplicationexponent
(how many times
it’s multiplied)3 • 3 • 3 • 3 can be written 3 432 as 3 to the 2nd power or 3 squared23 means 2 • 2 • 2 and 2 • 2 • 2 = 852 means 5 • 5 NOT 5 • 2so 5^2 = 5 • 5 = 25 BUT 5 (^2) ‡ 10
Example
Simplify
2 • 2 • 2 • 2
(^169)
144
24 • 3^2
•
•
3 • 3
Explanation
Exponents mean multiplication.Simplified result is 144
(no exponents left)Use 2 as a factor 4 times.
Use 3 as a factor 2 times.
2 • 2 • 2 • 2 is 16
3 • 3 is 9 16 • 9 is 144(^33) as 3 to the 3rd power or 3 cubed
34 as 3 to the 4th power
etc.
base
(the number being multiplied)
Careful!
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